Question

With the Hall process, how many hours will it take to deposit \(664 \mathrm{~g}\) of \(\mathrm{Al}\) at a current of \(32.6 \mathrm{~A}\) ?

Short answer

The process takes about 60.74 hours.

Step-by-step solution

Understanding the Problem

We need to calculate the time required to deposit 664 g of Aluminum (Al) using the Hall process with a given current of 32.6 A. This requires an understanding of the relationship between mass, current, and time in electrochemical processes.

Use Faraday’s Law of Electrolysis

Faraday's law relates the amount of substance deposited at an electrode to the charge passed through the electrolyte. We use the formula \[ m = \frac{(I \cdot t \cdot M)}{z \cdot F} \]where \( m \) is the mass in grams, \( I \) is the current in Amperes, \( t \) is the time in seconds, \( M \) is the molar mass, \( z \) is the number of electrons exchanged, and \( F \) is Faraday's constant (96485 C/mol). For aluminum, \( M = 26.98 \, \text{g/mol} \) and \( z = 3 \).

Rearrange the Formula

To find time \( t \), rearrange the formula to \[ t = \frac{(m \cdot z \cdot F)}{(I \cdot M)} \]This will allow us to solve for \( t \) given the values for mass, current, molar mass, and number of electrons.

Substitute Given Values

Substitute the given values into the formula:\[ m = 664 \, \text{g}, \quad I = 32.6 \, \text{A}, \quad M = 26.98 \, \text{g/mol}, \quad z = 3, \quad F = 96485 \, \text{C/mol} \]This results in \[ t = \frac{(664 \, \text{g} \cdot 3 \cdot 96485 \, \text{C/mol})}{(32.6 \, \text{A} \cdot 26.98 \, \text{g/mol})} \]

Calculate Time in Seconds

Perform the calculation:\[ t = \frac{(664 \times 3 \times 96485)}{(32.6 \times 26.98)} = \frac{192438420}{879.548} \approx 218677.2 \, \text{s} \]

Convert Time to Hours

Convert the time from seconds to hours by dividing by 3600 (since one hour is 3600 seconds):\[ t_{\text{hours}} = \frac{218677.2}{3600} \approx 60.74 \, \text{hours} \]

Step

The time required is approximately 60.74 hours.

Key concepts

Hall process

The Hall process is an industrial technique used primarily for the production of aluminum. It involves dissolving alumina (\(\text{Al}_2\text{O}_3\)) in molten cryolite (\(\text{Na}_3\text{AlF}_6\)) and then electrolyzing it to extract pure aluminum metal. The electrolytic cell used in this process consists of a carbon anode and a carbon-lined cathode. When an electric current is passed through the solution, aluminum ions in the alumina are reduced and deposited at the cathode, while oxygen is released at the anode.
This process was developed in the late 19th century and revolutionized aluminum production, making it more efficient and economically viable. The role of electricity in the Hall process is crucial, as it facilitates the separation of aluminum from its oxide form, making this a prime example of electrochemical processing in metallurgy.

Electrochemical processes

Electrochemical processes are chemical reactions driven by electrical energy. In an electrochemical cell, chemical energy is converted into electrical energy or vice versa. These processes are fundamental to a wide range of technologies, including batteries, fuel cells, and electrolysis.
In the context of electrolytic deposition, such as the Hall process, electricity is used to drive a non-spontaneous chemical reaction. The application of a current causes ions to move and reactions to occur at the electrodes:

• At the cathode, reduction reactions take place, allowing metal ions from the solution to gain electrons and become solid metal deposits.
• At the anode, oxidation reactions occur, releasing electrons into the circuit.

This intricate play of chemical and electrical processes forms the basis of many industrial applications, including the extraction and refining of metals.

Molar mass calculation

Molar mass is a key concept in chemistry that represents the mass of one mole of a substance. It is expressed in grams per mole (\( ext{g/mol}\)) and is calculated by summing the atomic masses of all atoms in a molecule. This property is crucial when dealing with conversions between mass and moles in chemical reactions.
For example, the molar mass of aluminum (Al) is calculated based on its atomic mass, which is approximately 26.98 g/mol. When performing calculations involving Faraday's Law of Electrolysis, knowing the molar mass allows one to relate the amount of substance in moles to its physical mass. Thus, it is essential for determining how much of a substance will be produced or consumed in electrochemical processes.

Current and time relationship

The relationship between current and time is fundamental in electrochemical calculations. Current, measured in amperes (A), represents the flow of electric charge in a circuit. In an electrolytic process, the total charge passing through the electrolyte over time is a product of the current and the duration for which it is applied.
Through Faraday's laws, we understand that the amount of substance deposited at an electrode is directly proportional to the electric charge. The formula involves:

• Mass (\( m \)),
• Current (\( I \)),
• Time (\( t \)),
• Molar mass (\( M \)), and
• Faraday’s constant (\( F \)).

This formula offers a direct way to calculate any of these values if the others are known. It ultimately helps determine how long a process needs to run to achieve a desired amount of deposition, like calculating the 60.74 hours required for the deposition of 664 g of aluminum in the Hall process.